140 lines
3.7 KiB
Groff
140 lines
3.7 KiB
Groff
.\" Copyright (c) 1985, 1991 Regents of the University of California.
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.\" All rights reserved.
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.\"
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.\" Redistribution and use in source and binary forms, with or without
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.\" modification, are permitted provided that the following conditions
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.\" are met:
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.\" 1. Redistributions of source code must retain the above copyright
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.\" notice, this list of conditions and the following disclaimer.
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.\" 2. Redistributions in binary form must reproduce the above copyright
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.\" notice, this list of conditions and the following disclaimer in the
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.\" documentation and/or other materials provided with the distribution.
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.\" 3. All advertising materials mentioning features or use of this software
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.\" must display the following acknowledgement:
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.\" This product includes software developed by the University of
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.\" California, Berkeley and its contributors.
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.\" 4. Neither the name of the University nor the names of its contributors
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.\" may be used to endorse or promote products derived from this software
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.\" without specific prior written permission.
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.\"
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.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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.\" SUCH DAMAGE.
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.\"
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.\" from: @(#)hypot.3 6.7 (Berkeley) 5/6/91
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.\" $FreeBSD$
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.\"
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.Dd May 6, 1991
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.Dt HYPOT 3
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.Os
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.Sh NAME
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.Nm hypot ,
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.Nm hypotf ,
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.Nm cabs ,
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.Nm cabsf
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.Nd Euclidean distance and complex absolute value functions
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.Sh LIBRARY
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.Lb libm
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.Sh SYNOPSIS
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.In math.h
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.Ft double
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.Fn hypot "double x" "double y"
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.Ft float
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.Fn hypotf "float x" "float y"
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.In complex.h
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.Ft double
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.Fn cabs "double complex z"
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.Ft float
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.Fn cabsf "float complex z"
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.Sh DESCRIPTION
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The
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.Fn hypot
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and
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.Fn hypotf
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functions
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compute the
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sqrt(x*x+y*y)
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in such a way that underflow will not happen, and overflow
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occurs only if the final result deserves it.
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The
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.Fn cabs
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and
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.Fn cabsf
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functions compute the complex absolute value of
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.Fa z .
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.Pp
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.Fn hypot "\*(If" "v"
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=
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.Fn hypot "v" "\*(If"
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= +\*(If for all
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.Fa v ,
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including \*(Na.
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.Sh ERROR (due to Roundoff, etc.)
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Below 0.97
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.Em ulps .
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Consequently
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.Fn hypot "5.0" "12.0"
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= 13.0
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exactly;
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in general, hypot and cabs return an integer whenever an
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integer might be expected.
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.Pp
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The same cannot be said for the shorter and faster version of hypot
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and cabs that is provided in the comments in cabs.c; its error can
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exceed 1.2
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.Em ulps .
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.Sh NOTES
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As might be expected,
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.Fn hypot "v" "\*(Na"
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and
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.Fn hypot "\*(Na" "v"
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are \*(Na for all
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.Em finite
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.Fa v ;
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with "reserved operand" in place of "\*(Na", the
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same is true on a
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.Tn VAX .
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But programmers on machines other than a
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.Tn VAX
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(if has no \*(If)
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might be surprised at first to discover that
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.Fn hypot "\(+-\*(If" "\*(Na"
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= +\*(If.
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This is intentional; it happens because
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.Fn hypot "\*(If" "v"
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= +\*(If
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for
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.Em all
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.Fa v ,
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finite or infinite.
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Hence
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.Fn hypot "\*(If" "v"
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is independent of
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.Fa v .
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Unlike the reserved operand fault on a
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.Tn VAX ,
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the
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.Tn IEEE
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\*(Na is designed to
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disappear when it turns out to be irrelevant, as it does in
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.Fn hypot "\*(If" "\*(Na" .
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.Sh SEE ALSO
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.Xr math 3 ,
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.Xr sqrt 3
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.Sh HISTORY
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Both a
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.Fn hypot
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function and a
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.Fn cabs
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function
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appeared in
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.At v7 .
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